Apparatus and method for the complete characterization of optical devices including loss, birefringence and dispersion effects

ABSTRACT

In order to characterize the optical characteristics of a device, a source of light having a variable frequency with a polarization state which varies linearly with frequency is provided as an input to the device under test. The input light is also passed through a known reference path and is added to the light output from the device under test in a beam combiner. The combined light for the frequencies of interest is split into two orthogonal polarizations which are then detected in a spectral acquisition apparatus and supplied to a microprocessor. The spectral measurements are digitized and curve-fitted to provide optical power versus optical frequency curves. Fourier transforms of each of the curves are calculated by the microprocessor. From the Fourier transforms, the four arrays of constants are calculated for the Jones matrix characterizing the device under test.

This application claims priority from provisional application Ser. No.60/255,077 filed Dec. 14, 2000 and now abandoned.

BACKGROUND OF THE INVENTION

1. Field of Application

The present invention generally relates to the measurement of theoptical characteristics of optical waveguide devices and, in particular,relates to devices for characterizing the optical effect of variousdevices upon an optical system.

2. Discussion of Prior Art

Waveguide devices such as Bragg gratings, interleavers, couplers,isolators, etc. require accurate characterization if they are to be usedin deployable optical fiber networks. Generally this characterizationhas been accomplished using a few simple specifications such asinsertion loss, bandwidth, polarization dependent loss, etc. The devicesactually have responses that are significantly more complicated thatthese specifications can describe. Although the simplification of thecharacterization is necessary to allow for the use of interchangeableparts, and rational specifications for manufacturers to meet, obtaininga full and complete measurement of the device from which any desiredspecification can be calculated would have benefits to bothmanufacturers and their customers.

First of all, full device characterization would permit computer systemmodels that are much more accurate, and would inherently contain aspectsof the device that have not been explicitly specified. Second, in caseswhere manufacturers use different specifications, or consumers require anew set of specifications, devices could be accurately compared, or newspecifications developed from the complete measurement function storedin a database. For most devices this measurement function would consistof four complex functions that would occupy less than 200 kB of storage.Finally, if the complete characterization of the device can be achievedwith a single instrument, then final testing of devices would be greatlysimplified while remaining completely general.

It is worthwhile to describe some of the fundamental differences betweenthe characteristics of fiber-optic links, and fiber-optic components(excluding fiber). Fiber-optic links are generally very long (>50 km),and have very broad spectral features that vary on the scale of tens ofnanometers. Because of the great lengths involved and high launch powersused to over come the loss, nonlinear interactions of light in the fiberare of significant interests. These nonlinear properties are not easilyreduced to a simple transfer function matrix. In very long fiber-opticlinks such a submarine links, optical amplifiers are used to regeneratethe signal and overcome loss. These amplifiers often operate insaturation which is another non-linear effect not captured in a simpletransfer function matrix. Generally, fiber-optic links are not wellcharacterized by simple transfer functions.

The relatively short path lengths (<1 m) within fiber optic componentsprevents any significant non-linear behavior. Because many passivefiber-optic components are filters used to separate channels closelyspaced in wavelength, they are designed to have rapid variations intheir properties, as a function of wavelength. Optical filters oftendisplay variations on the scale of tens of picometers instead of tens ofnanometers as seen in fiber optic links. Not only does the transmissionamplitude of these functions vary rapidly, but the phase response doesas well, and so, in high bit-rate applications, the phase response mustbe accurately measured as well. Also, due to the fabrication techniques,many filters display some variation as a function of polarization.Again, in high bit-rate systems, this variation must be accuratelycharacterized. It is in these last two measurements, optical phase, andpolarization dependence, that the inventions presented here excel.

The underlying technology used was initially developed by Glombitza andBrinkmeyer, and published in 1993 (“Coherent Frequency-DomainReflectometry for Characterization of Single-Mode Integrated-OpticalWaveguides,” Journal of Lightwave Technology, Vol. 11, No. 8, August1993). No patents were filed by either author with regard to thistechnology. Patents of a similar nature are U.S. Pat. No. 5,082,368“Heterodyne optical time domain reflectometer,” which employed anacousto-optic modulator, and U.S. Pat. No. 4,674,872 “Coherentreflectometer,” which employed an optical phase shifter, and has expireddue to nonpayment of maintenance fees. A co-pending U.S. patentapplication Ser. No. 09/606,120 filed Jun. 16, 2000 by Froggatt andErdogan for an invention entitled “Single Laser Sweep Full S-ParameterCharacterization of Fiber Bragg Gratings,” herein incorporated byreference, expands upon the published and unpatented work by Glombitzaand Brinkmeyer to describe how the measurement of the phase andamplitude of the time domain response of a system can be used todetermine the frequency domain (spectral) response of the system as wellvia an inverse Fourier transform. U.S. Pat. No. 5,896,193 for “Apparatusfor testing an optical component” also describes an interferometer muchlike that described by Glombitza and Brinkmeyer although the patentfiling on February 14, 1997 post dates the Glombitza and Brinkmeyerarticle publication date of August 1993 by over three years.

The Jones Matrix Representation

An optical fiber component supporting two polarization modes can befully described using a wavelength dependent Jones matrix. This matrixdescribes the transfer of energy from the device input to the deviceoutput, encompassing the full effects of polarization dependence. TheJones Matrix relates the input electric field to the output electricfield by: $\begin{matrix}{\begin{bmatrix}E_{s,{out}} \\E_{p,{out}}\end{bmatrix} = {\begin{bmatrix}a & b \\c & d\end{bmatrix}\begin{bmatrix}E_{s,{in}} \\E_{p,{in}}\end{bmatrix}}} & {{Eqn}.\quad 1}\end{matrix}$where E_(S) and E_(P) are complex electric field amplitudes of the twoorthogonal fields used to represent the total electric field. Theseorthogonal fields may be any orthogonal state and linear states orientedat 90 degrees are the most common. However, left hand and right hand 9circular would be an equally valid choice. No particular pair oforthogonal states is needed for the present invention.

This four element two-by-two matrix is completely general and includesall aspects of the device behavior. If the four complex numbers (a, b, c& d) can be measured as a function of frequency, then the device hasbeen completely characterized. It is therefore an object of thisinvention to measure these four quantities, and from this basic physicalmeasurement derive any and all of the desired parameters describing thedevice.

SUMMARY OF THE INVENTION

It is an object of the present invention to supply a controlled lightinput to a fiber optic device and then compare the output from thedevice with the input to characterize the effect of the device on suchlight.

In the broadest sense, the present invention involves the supplying oflight having an optical frequency content over the frequency range ofinterest where the light has a polarization state which varies linearlywith the frequency. This light is provided to the device under test. Thelight is affected by the device and is output therefrom. The affectedoutput light is combined in a combiner with the input light over thefrequency range of interest. The combined light from the combiner isdetected and digitized over a plurality of measurements in the frequencyrange. A microprocessor derives power curves from the digitized combineroutput. The microprocessor calculates the Fourier transform of therespective curves and derives from the Fourier transforms four arrays ofconstants for the Jones matrix characterizing the device.

In a specific embodiment, a source of variable frequency light whichcould be a tunable frequency laser is provided where the light has asimilar polarization. The light is supplied to a “spinner” whichprovides output light having a polarization which varies linearly withthe changing frequency of the light. The light from the spinner issupplied as an input to the device under test and also to a beamcombiner. The resultant light from the device under test is alsosupplied to the input of the combiner and its output is supplied to apolarization beam splitter. After having the combined light split intotwo orthogonal polarization states, the two orthogonally polarized beamsof light are supplied to respective detectors. The outputs from thedetectors is digitized over a plurality of measurements taken atdiffering frequencies and respective curves power are derived Aprogrammed microprocessor calculates the Fourier transform for each ofthe curves and derives four arrays of constants for a Jones matrixcharacterizing the device under test.

BRIEF DESCRIPTION OF THE DRAWINGS

In order that the present invention may be more clearly understood,examples of various embodiments thereof may be described by reference tothe following drawings, in which:

FIG. 1 is a block diagram showing a generic version of the presentinvention;

FIG. 2 is a schematic view of a spinner according to one embodiment ofthe present invention;

FIG. 3 is an illustration of a series of graphs of polarization versusfrequency for the light exiting the polarization beam combiner;

FIG. 4 is a representational view of the polarization states viewed on aPoincaré sphere;

FIG. 5 is a schematic representation of a fiber-optic tunable lasermonitoring network;

FIG. 6 is a schematic of the fiber-optic network used to create theinterference fringes needed to determine the Jones Matrix for the DeviceUnder Test (DUT).

FIGS. 7A and 7B are comparison of graphs of detected signal amplitudeversus frequency for the s and p detectors for a “nulled” alignment;

FIGS. 8A and 8B are comparison of graphs of detected signal amplitudeversus frequency for the s and p detectors for a “maximized” alignment;

FIG. 9 is a schematic showing the optical path and associated losslesstranslation matrices;

FIG. 10 is a schematic of one embodiment of the present invention withthe Device Under Test;

FIG. 11 is a schematic of a single-mode (SM) fiber spinner module;

FIG. 12 is block diagram of a double spinner embodiment of the presentinvention;

FIG. 13 is a schematic of one embodiment of the invention shown in FIG.12;

FIG. 14 is a graph of amplitude versus frequency of Fourier transformsof interference in the L2 and L3 interferometers;

FIG. 15 is a graph of amplitude versus frequency for Fourier transformsof interference fringes at the detector;

FIG. 16 is a schematic of a further embodiment of the present invention;

FIG. 17 is a schematic of a still further embodiment of the presentinvention; and

FIG. 18 is a schematic of a portion of the network of the inventionillustrating calibration of the system.

DETAILED DISCUSSION OF EMBODIMENTS

For simplicity of understanding, similar components will be similarlynumbered throughout the several views.

The inventions described here can readily measure the matrix above,however, the basis vectors used to describe the electric field is leftunknown. This topic, and the reason that it can be neglected isdescribed in the section “Unitary Translation and PolarizationCharacteristics”.

Unitary Translation and Polarization Characteristics

Telecommunications systems use optical fiber that supports twopolarization modes. Some effort has been expended to developsingle-polarization mode optical fiber, but the losses remained too highto permit their use in long-distance transmission systems, and so, twoat, polarization modes are supported in all currently installedfiber-optic links, and will continue to be supported in all linksinstalled in the foreseeable future.

A “supported” mode is one that will propagate over long distances. Thetwo modes supported in telecom links can be described as “degenerate”meaning that light in each mode propagates down the fiber at nearly thesame speed. The difference in the speed of propagation between the modesis referred to as polarization-mode-dispersion. For short lengths ofoptical fiber (<100 m), this difference in propagation velocity is sosmall that the delay difference is essentially zero. Over very longtransmission distances (>50 lm), the very small difference inpropagation speed can cause significant differences in the delay betweenpolarization modes. This accumulated difference now forms the barrier toincreased data rates in optical fiber. As a result, methods tocompensate for polarization mode dispersion are now at the center ofmany optical fiber communications research programs.

When the polarization-mode-dispersion in an optical fiber is kept small,the two modes are considered to be degenerate. A consequence ofdegeneracy is that energy can very easily move between the supportedmodes in the fiber. This freedom of movement between the supported modesin the optical fiber means that the polarization state in optical fiberis essentially uncontrolled. Mild bends, external stresses, and thermalchanges can all change the state of polarization of light in opticalfiber.

Although the input and output polarization states for a segment of fibercan be considered to be independent, the lossless nature of fibertransmission does impose some restrictions on the output state of thelight. First of all, the amplitude of the output light must be the sameas the input light (which is essentially the definition of lossless).Less obvious, but of great importance is the maintenance oforthogonality, i.e., when the dot product of two fields is zero.

Orthogonal polarization states do not interfere with one another, and bycombining the states in different phases and amplitudes, we canrepresent all states of polarization. Pairs of orthogonal states,therefore, represent an important physical construct. In a losslesssystem, such as an optical fiber, orthogonal inputs result in orthogonaloutputs. Any section of optical fiber can then be modeled as a “unitarytranslation.”

What does the concept of unitary translation mean to optical fibersystems? A good analogy is that of a three dimensional object in spacethat is rotated. Take for instance, a cat. If I have a cat and rotate itby some amount left to right, and then another amount front to back,potentially every point on the cat changes location, however, all of theimportant properties about the cat remain the same. Equivalently, if anarbitrary section of optical fiber is placed between an instrument and adevice, the measurement of the device is rotated by two unknown angles,but the properties of the device are all measured correctly. And becausepolarization states are not controlled in fiber-optic communicationssystems, the end user of the device cannot be certain of the device's“orientation” (with respect to the incident polarization) in the system,and must be assured that the device will work for all orientations. Theconcept of unitary translation can be extended further to measurementerror. Any measurement error that can be represented as a multiplicationby unitary matrices then becomes irrelevant to the measurement. Theability to fold such measurement errors, or unknowns, into the unknownfiber lead is what allows the present invention to be constructed in atractable and economical way.

FIG. 1 is a block diagram of a generic version of an optical vectoranalyzer in accordance with the present invention. The device under test(DUT) 10 is supplied with light from source 12 (indicated by the dottedline box) where the light has an optical frequency content over thefrequency range of interest (for the particular DUT) and the light has apolarization state which varies linearly with the frequency. In onepreferred embodiment, the light supplied by the source 12 is provided byan optical source 14 (either a narrow linewidth source such as a tunablelaser tunable over the bandwidth of interest or a broadband source oflight including the bandwidth of interest) which supplies light to thedevice entitled “spinner” 16 (discussed in detail below), which providesthe light with a polarization state which varies linearly with thefrequency. In one embodiment the source 14 is a narrow linewidth tunablesource such as a tunable laser, or a broadband source such as an LED orincandescent filament light. Although optical fiber is shown in thevarious drawings, it is understood that it could be replaced by afree-space collimated beam. Additionally, while couplers (indicated byellipses) are used, the could be replaced by bulk-optic beam splitters.

The spinner 16 causes the state of polarization of the light to rotatethrough a great circle around the Poincané sphere as function ofwavelength. The relationship between the angular change of thepolarization state thought the great circle and the frequency of thelight must be linear. The period of the variation (i.e. the frequencychange needed for 2 pi rotation) must be greater than the spectralresolution of the acquisition system. In the case of a tunable lasersource, this is the instantaneous linewidth of the source, and, in thecase of an OSA (Optical Spectrum Analyzer, a widely used commerciallyavailable device), this is the resolution bandwidth of the OSA.

The output from source 12 is provided to a reference path 18 and to theinput of the DUT 10. The reference path is a method of transmitting someportion of the light from the source 12 to the beam combiner 20. Thispath must have a Jones Matrix with a determinant that is not close tozero. In other words, this path cannot be a polarizer, and, ispreferably a lossless optical transmission such as a fiber, but it neednot be perfectly or substantially lossless. The matrix of the referencepath must be invertible in a practical sense. The transmission path tothe DUT need only satisfy the same criteria as the reference pathmatrix. The transmission path from the DUT should be substantiallylossless, or lossless to the degree of the accuracy required by themeasurement.

The output of the DUT 10 along with the output of the reference path 18is supplied to the input of a beam combiner 20 (indicated by dotted linebox). The combiner adds the light output from the DUT 10 and thereference path 18 for a plurality of frequencies in the frequency rangeof interest and splits the sum into two orthogonal polarizations. Inpreferred embodiments, the beam combiner 20 can be a coupling structure22, such as a bulk-optic beam splitter or a fused tapered coupler, whichsupplies a combined light signal to a polarizer 24 which breaks thefield into two orthogonal polarization states.

The two orthogonal polarizations from beam combiner 20 are supplied tothe microprocessor 26 (indicated by dotted line box). In a preferredembodiment, the microprocessor 26 includes a spectral acquisition device28 and a mathematical processor 30. The function of the spectralacquisition device 28 is to measure the power as a function ofwavelength of the two signals from the polarizer. These signals may beacquired sequentially or in parallel depending upon the application andembodiment. The spectral acquisition device 28, if the optical source isa narrow linewidth tunable source such as a laser, will be a pair ofdetectors from which the power is sampled as a function of the frequencyof the tunable source. Also, if the source is a narrow linewidth tunablesource, then it may be necessary to send a small part of the light fromthe source to the spectral acquisition unit so that the wavelength maybe accurately measured (as shown by the dotted line 13 connecting source12 and microprocessor 26 in FIG. 1). If the source is a broadbandoptical source, then the spectral acquisition device 28 will need to bea spectral measurement system such as an OSA. If the spectralmeasurement is made by an OSA, then it will not be necessary to send aportion of the light from the source to the OSA.

The mathematical processing unit 30 includes a digitizer to convert thespectral measurements made in device 26 to digital form if necessary andis programmed to derive curves fitting the spectral outputs, where thecurves are optical power versus optical frequency curves. Fouriertransforms of each of the curves are calculated by the processor. Fromthe Fourier transforms, four arrays of constants for a Jones matrixcharacterizing the DUT are calculated. Knowing the four arrays ofconstants of a Jones Matrix for the DUT allows total knowledge of howand in what fashion any device under test will affect an input signaland thus affect a fiber optic system.

Details of the “spinner” 16 are shown in FIG. 2 and comprises anfiber-optic network constructed from Polarization Maintaining (PM) fiber32, a splitter such as a PM coupler 34, a polarization beam combiner 36.In this embodiment the optical source 14 is a tunable laser which isdesirable because the power vs. wavelength will be initially measured in10 to 50 femtometer steps. The light from the laser is coupled to thepolarization maintaining fiber 32 such that all of the light is in asingle polarization mode. The light is then evenly split, using thepolarization maintaining (PM) coupler 34. Half of the light travelsthrough a long path Lp, and half of the light travels through a shortpath Sp. Light from the two paths is then recombined using thepolarization spinner 36.

The spinner 16 puts the light from one path into the x-polarization, andlight from the other path into the orthogonal y-polarization. Becausethe path lengths of the two components are unequal, the relative phasebetween the x-polarized light and the y-polarized light is stronglywavelength dependent As a result the polarization state of the lightexiting the polarization beam combiner 36 varies from linear toelliptical to right hand circular to elliptical, etc. as shown in the 9graphs of FIG. 3. Graph 1 illustrates the evolution of the polarizationstate of the light exiting the polarization beam combiner 36. The curvesshow the path that the electric field of the light traverses at opticalfrequencies. Note that the states include both circular polarizationstates, and two orthogonal linear states.

If the polarization state is viewed on the Poincaré sphere as shown inFIG. 4, it will trace a great circle through the poles of the sphere. Asthe light passes through the fiber following the beam splitter, thepolarization states will be changed. The changes in polarization causedby the single-mode fiber will be lossless, and as a consequence, thestates will always trace a great circle. As shown in FIG. 4, thePoincaré sphere representation of the states through which the lightexiting the polarization-beam-combiner traverses as the laser is tuned.The great circle traversed by the light has poles that are defined bythe states of polarization of the light in each of the “spinner” arms.The resultant light output on the single mode (SM) fiber from combiner36 of the spinner 16 has a polarization state which varies linearly withthe frequency of the light input to the spinner.

In order to monitor the source of light, in a preferred embodiment someof the light exiting the polarization beam combiner 36 of the spinner 16is picked off by the single-mode coupler 38 as shown in FIG. 5. Thispicked off light is again split by a second single-mode coupler 39 (forexample a 90/10 couple) and provides two light samples. One light sample(90% of the original beam) is used to trigger the acquisition of powerat the final signal detectors in the spectral acquisition block 28 withthe trigger detector 50. The trigger signal is generated by passing thelight through a long Michelson interferometer 40 comprised of coupler42, the trigger length of fiber Lt, and the two Faraday Rotator Mirrors(FRM's) 44. FRM's 44 are used in the interferometer to preventpolarization fading. In addition, the other light sample (10% of theoriginal beam) is passed through a reference gas cell 46 and gas celldetector 48 to calibrate the laser wavelength to a National Institutesof Standards and Technology (NIST) traceable standard every sweep.

FIG. 5 illustrates the elements making up the spectral acquisition block28 as shown by the dotted line. In FIG. 1, where the light sample isprovided to the spectral acquisition block 28 along the dotted line 13,such line is shown in FIG. 5 as the line connecting HA, couplers 38 &39. In FIG. 5, the Michelson interferometer 40 is connected to thetrigger detector 50 which produces sampling signals at very precisefrequency intervals. The FRM's 44 prevent fringe fading for fiberpositions. The Gas Cell 46 serves as a NIST traceable standard for boththe frequency increment of the Michelson interferometer trigger, and theabsolute wavelength of the measurement. As shown, the light that is notpicked off is split by a 50/50 coupler 41 (also known as a 3 dB coupler)and passed both through the DUT 10, and the reference path 18.

FIG. 6 is a specific form of the generic invention shown in FIG. 1. Thelight from the two paths is then recombined in the coupler 22 in apreferred embodiment using a single-mode coupler 43. The recombinedlight is then passed to the polarizer 24 which includes an all-fiberpolarization controller 52. This controller 52 forms an arbitrarylossless matrix that transforms one polarization state to another,without loss. The polarization controller could be located at anyposition between the spinner and the beam splitter 54 (except for alongthe DUT path). This transformation constitutes a “mapping” function.Adjusting the controller changes this matrix, but maintains its losslessnature. Mapping transforms the great-circle circumscribed on thePoincaré-sphere by the incident light to any other great circle. Afterpassing through the polarization controller 52, the recombined light isthen incident on a polarization-beam-splitter 54. At the beam splitter54, the light is split into its x- and y- polarization components. Thesecomponents are then incident on the s and p detectors 56 and 58,corresponding to the x and y components, respectively.

While the detectors 56 & 58 are shown outside of the dotted lineencompassing the polarizer 24, they could be included within thepolarizer and their output signal provided to the spectral acquisitionblock 28 as shown in FIG. 5. Alternatively, they could be included inthe spectral acquisition block 28. The location is not important-justthe fact that the output of the detectors 56 & 58, along with theoutputs of the trigger detector 50 and the gas cell detector 48, areprovided to the microprocessor 26.

The polarization controller 52 can be adjusted to one of two possiblealignments. The adjustment should be made with no light coming throughthe measurement path. In one polarization controller alignment-referredto as the “nulled alignment”-the two linear polarization states aremapped to the two linear polarization states of thepolarization-beam-splitter 54 when they pass through the reference path.In this alignment, the relative phase of the two states of polarizationat the polarization-beam-coupler 43 does not affect the power splittingratio at the polarization-beam-splitter 54 for reference path light, andas a result, no fringes are observed when the laser is tuned.

In the other polarization controller alignment-referred to as the“maximum contrast alignment”-the great circle circumscribed by thereference light is made to intersect with the two linear polarizationstates of the beam splitter 54. Whenever the reference polarizationstate passes through one of the linear states of the beam splitter, allof the reference power is incident on one detector, and none is incidenton the other detector. The reference power then oscillates between the sand p detectors 56 & 58, respectively, going to zero on one detectorwhen the power is maximized on the other detector. This output in apreferred embodiment is provided to the spectral acquisition unit 28.

If we look at the Fourier transform of the fringes, we get a time domainresponse, with the time domain response of each Jones matrix elementarriving at a different time. By properly selecting the complex valuedpoints associated with each matrix element, we can then use an inverseFourier transform to compute the frequency domain (spectral) Jonesmatrix elements. While each term is multiplied by a phase error, theresult of this phase error is equivalent to an arbitrary section oflossless optical fiber added to the device, and thus has no effect onthe measured properties of the device.

FIGS. 7A and 7B are illustrations of the amplitude versus frequency ofthe Fourier Transform of the interference fringes measured by thenetwork in FIG. 6 for the “nulled” alignment. FIGS. 8A and 8B areillustrations of the amplitude of the Fourier Transform of theinterference fringes measured by the network in FIG. 6 for the“maximized” alignment.

Theoretical Analysis

We can begin by representing the DUT or “device” as a simple diagonal2×2 matrix with complex, frequency-dependent entries, $\begin{matrix}{\overset{\overset{\_}{\_}}{M_{D}} = \begin{bmatrix}{m_{1}(\omega)} & 0 \\0 & {m_{2}(\omega)}\end{bmatrix}} & {{Eqn}.\quad 2}\end{matrix}$

In order to measure the complete response of the DUT, it is necessarythat two orthogonal polarizations be incident upon the device. Thesestates cannot be incident simultaneously, because the linearsuperposition of these states will form a new, single polarization. Inorder to perform a rapid measurement that will completely characterizethe device, it is desirable to use a polarization state that changesrapidly with frequency, such that the device response does notappreciably change for one complete cycle through polarization states.An optical device to produce this rapidly varying polarization using aPM splitter and a polarization spinner 36, has previously been disclosedin FIG. 2 as a “spinner” and would cost on the order of about $3000.

In the “spinner” of FIG. 2, the fiber-optic network produces apolarization state that is strongly dependent on wavelength. The use ofPolarization Maintaining (PM) fiber and a polarization beam coupler 43guarantees orthogonality of the recombined states, and results in awell-defined set of states through which the polarization evolves as thefrequency of the light is changed.

The normalized field emerging from this device is then given by,$\begin{matrix}{E_{0} = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\e^{{- i}\quad{\omega\tau}_{p}}\end{bmatrix}}} & {{Eqn}.\quad 3}\end{matrix}$

In order to meet the criteria above that the polarization state varyrapidly enough that the response of the DUT does not change appreciablythrough a single cycle, the delay, τ_(p), in the network above must begreater than the impulse response length of the device, τ_(h). The fibernetwork that transfers this field from the 50/50 beam splitter 41 to theDUT will have largely uncontrollable polarization properties. It isdesirable to impose two restrictions on this network. First, it have noPolarization Dependent Loss (PDL), and second, the matrix describing thenetwork be constant as a function of frequency over the range offrequencies that is of interest. Of these two requirements, the zero PDLcriteria is the most difficult to satisfy. The matrix for such a networkis, $\begin{matrix}{\overset{\overset{\_}{\_}}{M_{T}} = {\begin{bmatrix}{e^{i\quad\phi}\cos\quad\theta} & {{- e^{i\quad\psi}}\sin\quad\theta} \\{e^{i\quad\psi}\sin\quad\theta} & {e^{{- i}\quad\phi}\cos\quad\theta}\end{bmatrix}e^{{- i}\quad\omega\quad\pi_{T}}}} & {{Eqn}.\quad 4}\end{matrix}$There will be an arbitrary lossless matrix between the polarizationspinner 36, and the device, and then a second arbitrary lossless matrixbetween the device and the polarizing beam splitter 54, and so the totalresponse matrix is given by,{double overscore (M_(R))}={double overscore (M_(T2))}·{double overscore(M_(D))}·{double overscore (M_(T1))}  Eqn. 5which yields a new matrix in which each entry may be nonzero,$\begin{matrix}{\overset{\overset{\_}{\_}}{M_{R}} = \begin{bmatrix}a & b \\c & d\end{bmatrix}} & {{Eqn}.\quad 6}\end{matrix}$

FIG. 9 is an illustration of the optical path and some associatedlossless translation matrices (rot [1], rot [2], and rot [3]). Theelectric field also undergoes a translation through a lossless matrixfrom the spinner 16 to the polarizing beam splitter 54. This referencefield is then given by, $\begin{matrix}{{\overset{\_}{E}}_{ref} = {{\begin{bmatrix}{e^{i\quad\phi}\cos\quad\theta} & {{- e^{{- i}\quad\psi}}\sin\quad\theta} \\{e^{i\quad\psi}\sin\quad\theta} & {e^{i\quad\phi}\cos\quad\theta}\end{bmatrix}\begin{bmatrix}1 \\e^{i\quad\omega\quad\tau_{p}}\end{bmatrix}}\frac{e^{{- i}\quad\omega\quad\tau_{ref}}}{2}}} & {{Eqn}.\quad 7}\end{matrix}$The measured field is given by, $\begin{matrix}{{\overset{\_}{E}}_{meas} = {{\begin{bmatrix}a & b \\c & d\end{bmatrix}\begin{bmatrix}1 \\{\mathbb{e}}^{{- {\mathbb{i}}}\quad\omega\quad\tau_{p}}\end{bmatrix}}\frac{{\mathbb{e}}^{{- {\mathbb{i}}}\quad\omega\quad\tau_{D}}}{4}}} & {{Eqn}.\quad 8}\end{matrix}$and the field at the beam splitter 54 is given by $\begin{matrix}{{\overset{\_}{E}}_{split} = {{{\begin{bmatrix}{{\mathbb{e}}^{{\mathbb{i}}\quad\phi}\cos\quad\theta} & {{- {\mathbb{e}}^{{- {\mathbb{i}}}\quad\psi}}\sin\quad\theta} \\{{\mathbb{e}}^{{\mathbb{i}}\quad\psi}\sin\quad\theta} & {{\mathbb{e}}^{{- {\mathbb{i}}}\quad\phi}\cos\quad\theta}\end{bmatrix}\begin{bmatrix}1 \\{\mathbb{e}}^{{- {\mathbb{i}}}\quad\omega\quad\tau_{p}}\end{bmatrix}}\frac{{\mathbb{e}}^{{- {\mathbb{i}}}\quad\omega\quad\tau_{ref}}}{2}} + {{\begin{bmatrix}a & b \\c & d\end{bmatrix}\begin{bmatrix}1 \\{\mathbb{e}}^{{\mathbb{i}}\quad\omega\quad\tau_{p}}\end{bmatrix}}\frac{{\mathbb{e}}^{{- {\mathbb{i}}}\quad\omega\quad\tau_{D}}}{4}}}} & {{Eqn}.\quad 9}\end{matrix}$Multiplying the vector and matrix in the first term gives,$\begin{matrix}{{\overset{\_}{E}}_{split} = {{\left\lbrack \quad\begin{matrix}{{{\mathbb{e}}^{{\mathbb{i}}\quad\phi}\cos\quad\theta} - {{\mathbb{e}}^{- {{\mathbb{i}}{({\psi + {\omega\quad\tau_{p}}})}}}\sin\quad\theta}} \\{{{\mathbb{e}}^{{\mathbb{i}}\quad\psi}\sin\quad\theta} + {{\mathbb{e}}^{- {{\mathbb{i}}{({\phi + {\omega\quad\tau_{p}}})}}}\cos\quad\theta}}\end{matrix} \right\rbrack\quad\frac{{\mathbb{e}}^{{- {\mathbb{i}}}\quad\omega\quad\tau_{ref}}}{2}} + {\quad{{\left\lbrack \quad\begin{matrix}a & b \\c & d\end{matrix} \right\rbrack\left\lbrack \quad\begin{matrix}1 \\{\mathbb{e}}^{{- {\mathbb{i}}}\quad\omega\quad\tau_{p}}\end{matrix} \right\rbrack}\quad\frac{{\mathbb{e}}^{{- {\mathbb{i}}}\quad\omega\quad\tau_{D}}}{4}}}}} & {{Eqn}.\quad 10}\end{matrix}$and the multiplying the vector and matrix in the second term gives,$\begin{matrix}{{\overset{\_}{E}}_{split} = {{\begin{bmatrix}{{{\mathbb{e}}^{{\mathbb{i}}\quad\phi}\cos\quad\theta} - {{\mathbb{e}}^{- {{\mathbb{i}}{({\psi + {\omega\quad\tau_{p}}})}}}\sin\quad\theta}} \\{{{\mathbb{e}}^{{\mathbb{i}}\quad\psi}\sin\quad\theta} - {{\mathbb{e}}^{- {{\mathbb{i}}{({\phi + {\omega\quad\tau_{p}}})}}}\cos\quad\theta}}\end{bmatrix}\quad\frac{{\mathbb{e}}^{{- {\mathbb{i}}}\quad\omega\quad\tau_{ref}}}{2}} + {\quad{\begin{bmatrix}{a + {b\quad{\mathbb{e}}^{{- {\mathbb{i}}}\quad\omega\quad\tau_{p}}}} \\{c + {d\quad{\mathbb{e}}^{{- {\mathbb{i}}}\quad\omega\quad\tau_{p}}}}\end{bmatrix}\frac{{\mathbb{e}}^{{- {\mathbb{i}}}\quad\omega\quad\tau_{D}}}{4}}}}} & {{Eqn}.\quad 11}\end{matrix}$The fields are then split at the beam splitter 54, and sent to separatedetectors 56, 58 for power measurement; these fields are given by,$\begin{matrix}{E_{s} = {{\left( {{{\mathbb{e}}^{{\mathbb{i}}\quad\phi}\cos\quad\theta} - {{\mathbb{e}}^{- {{\mathbb{i}}{({\psi + {\omega\quad\tau_{p}}})}}}\sin\quad\theta}} \right)\frac{{\mathbb{e}}^{{- {\mathbb{i}}}\quad\omega\quad\tau_{ref}}}{2}} + {\left( {a + {b\quad{\mathbb{e}}^{{- {\mathbb{i}}}\quad\omega\quad\tau_{p}}}} \right)\frac{{\mathbb{e}}^{{- {\mathbb{i}}}\quad\omega\quad\tau_{p}}}{4}}}} & {{Eqn}.\quad 12}\end{matrix}$and $\begin{matrix}{E_{p} = {{\left( {{{\mathbb{e}}^{{\mathbb{i}}\quad\psi}\sin\quad\theta} + {e^{- {i{({\phi + {\omega\quad\tau_{p}}})}}}\cos\quad\theta}} \right)\frac{e^{{- i}\quad\omega\quad\tau_{ref}}}{2}} + {\left( {c + {d\quad e^{{- i}\quad\omega\quad\tau_{p}}}} \right)\frac{e^{{- i}\quad\omega\quad\tau_{D}}}{4}}}} & {{Eqn}.\quad 13}\end{matrix}$A signal proportional to the power incident on the s-detector 56 isgiven by multiplying the field by its complex conjugate, $\begin{matrix}{{E_{s} \cdot E_{s}^{*}} = {\left\lbrack \quad{{\left( {{e^{i\quad\phi}\cos\quad\theta} - {e^{- {i{({\psi + {\omega\quad\tau_{p}}})}}}\sin\quad\theta}} \right)\frac{e^{{- i}\quad\omega\quad\tau_{ref}}}{2}} + {\left( {a + {b\quad e^{{- i}\quad\omega\quad\tau_{p}}}} \right)\frac{e^{{- i}\quad\omega\quad\tau_{D}}}{4}}} \right\rbrack \cdot \left\lbrack \quad{{\left( {{e^{{- i}\quad\phi}\cos\quad\theta} - {e^{i{({\psi + {\omega\quad\tau_{p}}})}}\sin\quad\theta}} \right)\frac{e^{i\quad\omega\quad\tau_{ref}}}{2}} + {\left( {a^{*} + {b^{*}e^{i\quad\omega\quad\tau_{p}}}} \right)\frac{e^{i\quad\omega\quad\tau_{D}}}{4}}} \right\rbrack}} & {{Eqn}.\quad 14}\end{matrix}$Expanding this gives, $\begin{matrix}{{E_{s} \cdot E_{s}^{*}} = {{\frac{1}{4}\left( {1 - {e^{i{({\psi + \phi + {\omega\quad\tau_{p}}})}}\cos\quad\theta\quad\sin\quad\theta} - {e^{- {i{({\psi + \phi + {\omega\quad\tau_{p}}})}}}\cos\quad\theta\quad\sin\quad\theta}} \right)} + {\frac{1}{16}\left( {{a}^{2} + {b}^{2} + {a\quad b^{*}e^{i\quad\omega\quad\tau_{p}}} + {a^{*}b\quad e^{{- i}\quad\omega\quad\tau_{p}}}} \right)} + {\frac{1}{8}\left( {{e^{i\quad\phi}\cos\quad\theta} - {e^{- {i{({\psi + {\omega\quad\tau_{p}}})}}}\sin\quad\theta}} \right)\left( {a^{*} + {b^{*}e^{i\quad\omega\quad\tau_{p}}}} \right)e^{i\quad{\omega{({\tau_{D} - \tau_{ref}})}}}} + {\frac{1}{8}\left( {{e^{{- i}\quad\phi}\cos\quad\theta} - {e^{{- i}\quad{({\psi + {\omega\quad\tau_{p}}})}}\sin\quad\theta}} \right)\left( {a + {b\quad e^{{- i}\quad\omega\quad\tau_{p}}}} \right)e^{{- i}\quad{\omega{({\tau_{D} - \tau_{ref}})}}}}}} & {{Eqn}.\quad 15}\end{matrix}$Reducing the expression to only its real parts, $\begin{matrix}{{E_{s} \cdot E_{s}^{*}} = {{\frac{1}{4}\left\lbrack {1 - {{\sin\left( {2\quad\theta} \right)}{\cos\left( {\psi + \phi + {\omega\quad\tau_{p}}} \right)}}} \right\rbrack} + {\frac{1}{16}\left( {{a}^{2} + {b}^{2} + {2{{Re}\left\lbrack {a\quad b^{*}{\mathbb{e}}^{{\mathbb{i}}\quad\omega\quad\tau_{p}}} \right\rbrack}}} \right)} + {\frac{1}{8}{{Re}\left\lbrack {\left( {{{\mathbb{e}}^{{\mathbb{i}}\quad\phi}\cos\quad\theta} - {{\mathbb{e}}^{- {i{({\psi + {\omega\quad\tau_{p}}})}}}\sin\quad\theta}} \right)\left( {a^{*} + {b^{*}{\mathbb{e}}^{{\mathbb{i}}\quad\omega\quad\tau_{p}}}} \right){\mathbb{e}}^{{\mathbb{i}}\quad{\omega{({\tau_{D} - \tau_{ref}})}}}} \right\rbrack}}}} & {{Eqn}.\quad 16}\end{matrix}$And then expanding the third term, $\begin{matrix}{{E_{s} \cdot E_{s}^{*}} = {{\frac{1}{4}\left\lbrack {1 - {{\sin\left( {2\quad\theta} \right)}{\cos\left( {\psi + \phi + {\omega\quad\tau_{p}}} \right)}}} \right\rbrack} + {\frac{1}{16}\left( {{a}^{2} + {b}^{2} + {2\quad{{Re}\left\lbrack {a\quad b^{*}{\mathbb{e}}^{{\mathbb{i}}\quad\omega\quad\tau_{p}}} \right\rbrack}}} \right)} + {\frac{1}{8}{{Re}\left\lbrack {\left( {{a^{*}{\mathbb{e}}^{{\mathbb{i}}\quad\phi}\cos\quad\theta} + {b^{*}{\mathbb{e}}^{{\mathbb{i}}\quad\omega\quad\tau_{p}}{\mathbb{e}}^{{\mathbb{i}}\quad\phi}\cos\quad\theta} - {{\mathbb{e}}^{- {{\mathbb{i}}{({\psi + {\omega\quad\tau_{p}}})}}}\sin\quad\theta\quad a^{*}} - {{\mathbb{e}}^{- {{\mathbb{i}}{({\psi + {\omega\quad\tau_{p}}})}}}\sin\quad\theta\quad b^{*}{\mathbb{e}}^{{\mathbb{i}}\quad\omega\quad\tau_{p}}}} \right){\mathbb{e}}^{{\mathbb{i}}\quad{\omega{({\tau_{D} - \tau_{ref}})}}}} \right\rbrack}}}} & {{Eqn}.\quad 17}\end{matrix}$And a little bit or reordering $\begin{matrix}{{E_{s} \cdot E_{s}^{*}} = {{\frac{1}{4}\left\lbrack {1 - {{\sin\left( {2\quad\theta} \right)}{\cos\left( {\psi + \phi + {\omega\quad\tau_{p}}} \right)}}} \right\rbrack} + {\frac{1}{16}\left( {{a}^{2} + {b}^{2} + {2\quad{{Re}\left\lbrack {a\quad b^{*}{\mathbb{e}}^{{\mathbb{i}}\quad\omega\quad\tau_{p}}} \right\rbrack}}} \right)} + {\frac{1}{4}{{Re}\left\lbrack {\left( {{a^{*}{\mathbb{e}}^{{\mathbb{i}}\quad\phi}\cos\quad\theta} - {b^{*}{\mathbb{e}}^{{- {\mathbb{i}}}\quad\psi}\sin\quad\theta} + {b^{*}{\mathbb{e}}^{{\mathbb{i}}{({\phi + {\omega\quad\tau_{p}}})}}\cos\quad\theta} - {a^{*}{\mathbb{e}}^{- {{\mathbb{i}}{({\psi + {\omega\quad\tau_{p}}})}}}\sin\quad\theta}} \right){\mathbb{e}}^{{\mathbb{i}}\quad\omega\quad{({\tau_{D} - \tau_{ref}})}}} \right\rbrack}}}} & {{Eqn}.\quad 18}\end{matrix}$Now, repeat for the p-polarization $\begin{matrix}{{E_{p} \cdot E_{p}^{*}} = {\quad{\left\lbrack {{\left( {{{\mathbb{e}}^{{\mathbb{i}}\quad\psi}\sin\quad\theta} + {{\mathbb{e}}^{- {{\mathbb{i}}{({\phi + {\omega\quad\tau_{p}}})}}}\cos\quad\theta}} \right)\frac{{\mathbb{e}}^{{- {\mathbb{i}}}\quad\omega\quad\tau_{ref}}}{2}} + {\left( {c + {d\quad e^{{- i}\quad\omega\quad\tau_{p}}}} \right)\frac{{\mathbb{e}}^{{- {\mathbb{i}}}\quad\omega\quad\tau_{D}}}{4}}} \right\rbrack \cdot {\quad\left\lbrack {{\left( {{{\mathbb{e}}^{{- {\mathbb{i}}}\quad\psi}\sin\quad\theta} +}\quad \right.\left. \quad{{\mathbb{e}}^{{\mathbb{i}}{({\phi + {\omega\quad\tau_{p}}})}}\cos\quad\theta} \right)\frac{{\mathbb{e}}^{{\mathbb{i}}\quad\omega\quad\tau_{ref}}}{2}} + {\left( {c^{*} + {d^{*}{\mathbb{e}}^{{\mathbb{i}}\quad\omega\quad\tau_{p}}}} \right)\frac{{\mathbb{e}}^{{\mathbb{i}}\quad\omega\quad\tau_{D}}}{4}}} \right\rbrack}}}} & {{Eqn}.\quad 19}\end{matrix}$expanding and collecting real parts, $\begin{matrix}{{E_{p} \cdot E_{p}^{*}} = {{\frac{1}{4}\left\lbrack {1 + {{\sin\left( {2\quad\theta} \right)}\quad\cos\quad\left( {\phi + \psi + {\omega\quad\tau_{p}}} \right)}} \right\rbrack} + {\frac{1}{16}\left\lfloor {{c}^{2} + {d}^{2} + {2\quad{{Re}\left\lbrack {{cd}^{*}{\mathbb{e}}^{{\mathbb{i}}\quad\omega\quad\tau_{p}}} \right\rbrack}}} \right\rfloor} + {2\quad{{Re}\left\lbrack {\frac{1}{8}\left\lbrack {\left( {{{\mathbb{e}}^{{\mathbb{i}}\quad\psi}\sin\quad\theta} + {{\mathbb{e}}^{- {{\mathbb{i}}{({\phi + {\omega\quad\tau_{p}}})}}}\cos\quad\theta}} \right)\left( {c^{*} + {d^{*}{\mathbb{e}}^{{\mathbb{i}}\quad\omega\quad\tau_{p}}}} \right){\mathbb{e}}^{{\mathbb{i}}\quad{\omega{({\tau_{D} - \tau_{ref}})}}}} \right\rbrack} \right\rbrack}}}} & {{Eqn}.\quad 20}\end{matrix}$expanding the third term again${E_{p} \cdot E_{p}^{*}} = {{\frac{1}{4}\left\lbrack {1 + {{\sin\left( {2\quad\theta} \right)}\cos\quad\left( {\phi + \psi + {\omega\quad\tau_{p}}} \right)}} \right\rbrack} + {\frac{1}{16}\left\lfloor {{c}^{2} + {d}^{2} + {2\quad{{Re}\left\lbrack {c\quad d^{*}{\mathbb{e}}^{{\mathbb{i}}\quad\omega\quad\tau_{p}}} \right\rbrack}}} \right\rfloor} + {\frac{1}{4}{{Re}\left\lbrack {\left( {{c^{*}{\mathbb{e}}^{\mathbb{i}\psi}\sin\quad\theta} + {d^{*}{\mathbb{e}}^{{\mathbb{i}\omega\tau}_{p}}{\mathbb{e}}^{- {{\mathbb{i}}{({\phi + {\omega\quad\tau_{p}}})}}}\cos\quad\theta} + {d^{*}{\mathbb{e}}^{{\mathbb{i}}\quad\omega\quad\tau_{p}}{\mathbb{e}}^{{\mathbb{i}}\quad\psi}\sin\quad\theta} + {c^{*}{\mathbb{e}}^{- {{\mathbb{i}}{({\phi + {\omega\quad\tau_{p}}})}}}\cos\quad\theta}} \right){\mathbb{e}}^{{\mathbb{i}}\quad{\omega{({\tau_{D} - \tau_{ref}})}}}} \right\rbrack}}}$and a final reordering $\begin{matrix}{{E_{p} \cdot E_{p}^{*}} = {{\frac{1}{4}\left\lbrack {1 + {\sin\quad\left( {2\quad\theta} \right)\quad\cos\quad\left( {\phi + \psi + {\omega\quad\tau_{p}}} \right)}} \right\rbrack} + {\frac{1}{16}\left\lbrack {{c}^{2} + {d}^{2} + {2{{Re}\left\lbrack {c\quad d^{*}{\mathbb{e}}^{{\mathbb{i}}\quad\omega\quad\tau_{p}}} \right\rbrack}}} \right\rbrack} + {\frac{1}{4}\quad{{Re}\left\lbrack {\left( {{c^{*}\quad{\mathbb{e}}^{{\mathbb{i}}\quad\psi}\quad\sin\quad\theta} + {d^{*}\quad{\mathbb{e}}^{{- {\mathbb{i}}}\quad\phi}\quad\cos\quad\theta} + {d^{*}\quad{\mathbb{e}}^{{\mathbb{i}}\quad{({\psi + {\omega\quad\tau_{p}}})}}\quad\sin\quad\theta} + {c^{*}{\mathbb{e}}^{{- {\mathbb{i}}}\quad{({\phi + {\omega\quad\tau_{p}}})}}\quad\cos\quad\theta}} \right)\quad{\mathbb{e}}^{{\mathbb{i}}\quad\omega\quad{({\tau_{D} - \tau_{ref}})}}} \right\rbrack}}}} & {{Eqn}.\quad 22}\end{matrix}$So, our detected powers for the p and s detectors 58 & 56, respectivelyare, $\begin{matrix}{{E_{s} \cdot E_{s}^{*}} = {{\frac{1}{4}\left\lbrack {1 - {\sin\quad\left( {2\quad\theta} \right)\quad\cos\quad\left( {\psi + \phi + {\omega\quad\tau_{p}}} \right)}} \right\rbrack} + {\frac{1}{16}\left( {{a}^{2} + {b}^{2} + {2{{Re}\left\lbrack {{ab}^{*}{\mathbb{e}}^{{\mathbb{i}}\quad\omega\quad\tau_{p}}} \right\rbrack}}} \right)} + {\frac{1}{4}\quad{{Re}\left\lbrack {\left( {{a\quad{\mathbb{e}}^{{- {\mathbb{i}}}\quad\phi}\quad\cos\quad\theta} - {b\quad{\mathbb{e}}^{{\mathbb{i}}\quad\psi}\quad\sin\quad\theta} + {b\quad{\mathbb{e}}^{{- {\mathbb{i}}}\quad{({\phi + {\omega\quad\tau_{p}}})}}\quad\cos\quad\theta} - {a\quad{\mathbb{e}}^{{\mathbb{i}}\quad{({\psi + {\omega\quad\tau_{p}}})}}\quad\sin\quad\theta}} \right)\quad{\mathbb{e}}^{{- {\mathbb{i}}}\quad\omega\quad{({\tau_{D} - \tau_{ref}})}}} \right\rbrack}}}} & {{Eqn}.\quad 23}\end{matrix}$and $\begin{matrix}{{E_{p} \cdot E_{p}^{*}} = {{\frac{1}{4}\left\lbrack {1 + {\sin\quad\left( {2\quad\theta} \right)\quad\cos\quad\left( {\phi + \psi + {\omega\quad\tau_{p}}} \right)}} \right\rbrack} + {\frac{1}{16}\left\lfloor {{c}^{2} + {d}^{2} + {2{{Re}\left\lbrack {c\quad d^{*}{\mathbb{e}}^{{\mathbb{i}}\quad\omega\quad\tau_{p}}} \right\rbrack}}} \right\rfloor} + {\frac{1}{4}\quad{{Re}\left\lbrack {\left( {{c\quad{\mathbb{e}}^{{- {\mathbb{i}}}\quad\psi}\quad\sin\quad\theta} - {d\quad{\mathbb{e}}^{{\mathbb{i}}\quad\psi}\quad\cos\quad\theta} + {d\quad{\mathbb{e}}^{{- {\mathbb{i}}}\quad{({\psi + {\omega\quad\tau_{p}}})}}\quad\sin\quad\theta} + {c\quad{\mathbb{e}}^{{\mathbb{i}}\quad{({\phi + {\omega\quad\tau_{p}}})}}\quad\cos\quad\theta}} \right)\quad{\mathbb{e}}^{{- {\mathbb{i}}}\quad\omega\quad{({\tau_{D} - \tau_{ref}})}}} \right\rbrack}}}} & {{Eqn}.\quad 24}\end{matrix}$

Here, we will digress a moment to discuss the parameter, θ, and whatmight be done about it. FIG. 10 is a schematic of a fiber-optic networkfor the measurement of the reflection response of a DUT. The paththrough the polarization controller 52 is the reference path. Thepolarization controller is adjusted so that the fringes measured at thedetectors are maximized. This adjustment must be made with the DUTdisconnected, and the laser sweeping. With the fringes maximized, thesystem is described as being “aligned.” An alternate alignment in whichthe fringes are nulled is also possible.

As shown in FIG. 10, we can insert a polarization controller 52 in thereference path, and use it to manipulate the polarization state of theincident field incident on the beam splitter.If we zero out the return signal from the device under test (bend thelead fiber), The fields incident on the detectors are $\begin{matrix}{{E_{s} \cdot E_{s}^{*}} = {\frac{1}{4}\left\lbrack {1 - {\sin\quad\left( {2\quad\theta} \right)\quad\cos\quad\left( {\psi + \phi + {\omega\quad\tau_{p}}} \right)}} \right\rbrack}} & {{Eqn}.\quad 25}\end{matrix}$and $\begin{matrix}{{E_{p} \cdot E_{p}^{*}} = {{\frac{1}{4}\left\lbrack {1 + {\sin\quad\left( {2\quad\theta} \right)\quad\cos\quad\left( {\phi + \psi + {\omega\quad\tau_{p}}} \right)}} \right\rbrack}.}} & {{Eqn}.\quad 26}\end{matrix}$

By adjusting the polarization controller 52 to achieve full contrast, θis set to {fraction (π/a)}+{fraction (qπ/2)} where q is an integer andrepresents an uncertainty in the sign of the trigonometric function. Thedetected fields are then given by, $\begin{matrix}{{E_{s} \cdot E_{s}^{*}} = {{\frac{1}{4}\left\lbrack {1 \pm {\cos\quad\left( {\psi + \phi + {\omega\quad\tau_{p}}} \right)}} \right\rbrack} + {\frac{1}{16}\left( {{a}^{2} + {b}^{2} + {2{{Re}\left\lbrack {{ab}^{*}{\mathbb{e}}^{{\mathbb{i}}\quad\omega\quad\tau_{p}}} \right\rbrack}}} \right)} + {\quad{\frac{1}{4\quad\sqrt{2}}\quad{{Re}\left\lbrack {\left( {{a\quad{\mathbb{e}}^{{- {\mathbb{i}}}\quad{({\phi + {k\quad\pi}})}}} - {b\quad{\mathbb{e}}^{{\mathbb{i}}\quad{({\phi + {l\quad\pi}})}}} + {b\quad{\mathbb{e}}^{{- {\mathbb{i}}}\quad{({\phi + {k\quad\pi} + {\omega\quad\tau_{p}}})}}} - {a\quad{\mathbb{e}}^{{\mathbb{i}}\quad{({\psi + {l\quad\pi} + {\omega\quad\tau_{p}}})}}}} \right)\quad{\mathbb{e}}^{{- {\mathbb{i}}}\quad\omega\quad{({\tau_{D} - \tau_{ref}})}}} \right\rbrack}}}}} & {{Eqn}.\quad 27}\end{matrix}$and $\begin{matrix}{{E_{p} \cdot E_{p}^{*}} = {{\frac{1}{4}\left\lbrack {1 \mp {\cos\quad\left( {\phi + \psi + {\omega\quad\tau_{p}}} \right)}} \right\rbrack} + {\frac{1}{16}\left\lbrack {{c}^{2} + {d}^{2} + {2{{Re}\left\lbrack {c\quad d^{*}{\mathbb{e}}^{{\mathbb{i}}\quad\omega\quad\tau_{p}}} \right\rbrack}}} \right\rbrack} + {\frac{1}{4\quad\sqrt{2}}\quad{{Re}\left\lbrack \left( {{c\quad{\mathbb{e}}^{{- {\mathbb{i}}}\quad{({\psi - {l\quad\pi}})}}} + {d\quad{\mathbb{e}}^{{\mathbb{i}}\quad{({\phi - {k\quad\pi}})}}} + {d\quad{\mathbb{e}}^{{- {\mathbb{i}}}\quad{({\psi - {l\quad\pi} + {\omega\quad\tau_{p}}})}}} + {{\quad\quad}\left. \quad\quad{c\quad{\mathbb{e}}^{{\mathbb{i}}\quad{({\phi - {k\quad\pi} + {\omega\quad\tau_{p}}})}}} \right)\quad{\mathbb{e}}^{{- {\mathbb{i}}}\quad\omega\quad{({\tau_{D} - \tau_{ref}})}}}} \right\rbrack \right.}}}} & {{Eqn}.\quad 28}\end{matrix}$where k and l are arbitrary integers.

Examining these detected signals it can be seen that the elements of thematrices have been shifted to separate locations in frequency space,with a phase shift. The relative phases between the elements in a Jonesmatrix are important and must be known to some degree as discussedlater. So, by selecting terms based upon their location in frequencyspace, and, also making a best guess at the polarization spinner delay,r, we can extract the following field responses,E _(a) =ae ^(i(Ψ+lπ+ωΔτ) ^(p) ⁾  Eqn. 29E _(b) =be ^(−i(φ+kπ+ωΔτ) ^(p) ⁾  Eqn. 30E _(ba) =ae ^(−t(φ+kπ)) −be ^(i(Ψ+1π))  Eqn. 31E _(c) =ce ^(i(φ−kπ+ωΔτ) ^(p) ⁾  Eqn. 32E _(d) =de ^(−i(Ψ−lπ+ωΔr) ^(p) ⁾  Eqn. 33E _(dc) =ce ^(−i(Ψ−lπ)) de ^(i(φ−kπ))  Eqn. 34where we have allowed for an error in our estimate of the spinner delayof Δτ_(p). We immediately have expressions for all of the matrixelements, however, an arbitrary phase factor, some of it frequencydependent, is associated with the phase factor.a=−E _(n) e ^(−i(Ψ+lπ+ωΔτ) ^(p) ⁾  Eqn. 35b=E _(b) e ^(i(φ+kπ+ωΔτ) ^(p) ⁾  Eqn. 36c=E _(c) e ^(−i(φ−kπ+ωΔτ) ^(p) ⁾  Eqn. 37 d=E _(d) e ^(i(Ψ−lπ+ωΔτ) ^(p) ⁾  Eqn. 38

Since we maximized the fringes that oscillate at a frequency of ωτ_(p),we can easily determine τ_(p), for each scan, thus allowing forvariations in the spinner path imbalance from scan to scan due totemperature. With the ωτ_(p) term removed from the exponents, and anystatic phase error lumped into Ψ and φ, we can then construct thematrix, $\begin{matrix}{\begin{bmatrix}{a\quad{\mathbb{e}}^{{- {\mathbb{i}}}\quad{({\phi + {k\quad\pi}})}}} & {b\quad{\mathbb{e}}^{{\mathbb{i}}\quad{({\psi + {l\pi}})}}} \\{c\quad{\mathbb{e}}^{{- {\mathbb{i}}}\quad{({\phi - {l\quad\pi}})}}} & {d\quad{\mathbb{e}}^{{\mathbb{i}}\quad{({\phi + {k\quad\pi}})}}}\end{bmatrix} = {\quad{{\begin{bmatrix}{\mathbb{e}}^{{\mathbb{i}}\quad\frac{\phi - \psi + {{({k - l})}\quad\pi}}{2}} & 0 \\0 & {\mathbb{e}}^{{\mathbb{i}}\quad\frac{\phi - \psi + {{({k - l})}\quad\pi}}{2}}\end{bmatrix}\begin{bmatrix}a & b \\c & d\end{bmatrix}}\begin{bmatrix}{\mathbb{e}}^{{\mathbb{i}}\quad\frac{\phi + \psi + {{({k + l})}\quad\pi}}{2}} & 0 \\0 & {\mathbb{e}}^{{\mathbb{i}}\quad\frac{\phi + \psi + {{({k + l})}\quad\pi}}{2}}\end{bmatrix}}}} & {{Eqn}.\quad 39}\end{matrix}$

Note that the measured matrix can be obtained from the original matrixby multiplication with two unitary matrices. This is not atransformation of basis, because the two matrices are not inverses ofone another. As a result, diagonalizing the measured matrix does notrecover the original matrix. All of the important properties of thematrix, Polarization Mode Dispersion, Polarization Dependent Loss,Spectral Amplitude and Group Delay are all maintained. All that has beenaltered is the polarization state at which a given minimum or maximumwill occur. Since polarization in optical fiber is rarely wellcontrolled, this loss of information regarding the device is notdetrimental to the vast majority of applications.

In the following embodiments, the mathematics describing the deviceperformance is not substantially altered, although the elements used toimplement the measurement are altered. These alterations involve theremoval of elements from claims and are not obvious.

No Polarization-Maintaining Fiber Embodiment

The embodiment described above in FIGS. 1 and 10 contains a PM fibercoupler 22. Proper operation of the device requires that the splittingratio of the coupler be very well matched. Obtaining PM couplers isdifficult and expensive. Obtaining well matched PM couplers is much moredifficult and expensive. Polarization-beam-combiners are also difficultand expensive to come by. It would, therefore, be advantageous toeliminate these elements from the invention, and replace them with moreeasily obtainable devices.

At the polarization beam combiner 20, the great circle on the Poincarésphere through which the polarization state rotates is well defined.Once the light has propagated through a few meters of optical fiber,however, the fiber will have transferred the polarization states to anew and completely arbitrary great circle. As a result, the well definedstates produced by the PM fiber system serve no useful purpose to themeasurement. We are then free to choose any set of orthogonal states tosend through the two different length paths.

As disclosed in U.S. Pat. No. 4,389,090 “Fiber Optic PolarizationController,” describes a simple apparatus that can be used to map anyinput polarization state to any other polarization state with little orno loss and little wavelength dependence. The polarization controllerconsists of three fiber loops that can be tilted independently, and isgenerally referred to as a set of LeFevre Loops after the inventor.

If we include a polarization controller of any kind (such as the LeFevreLoops discussed above) in a Mach-Zender Interferometer, we can adjustthe controller such that the two states, when recombined at the coupler,are orthogonal to one another. This state of orthogonality is achievedby adjusting the polarization controller until one output of the couplershows no fringes as the laser is tuned. The lack of interference fringesindicates that the two states of polarization entering the couplerthrough different paths have no common components, and are, therefore,orthogonal. With the creation of a polarization state that rotatesrapidly through a: great circle on the Poincaré sphere as a function ofwavelength, we have achieved an equivalent function to the PM fiber/polarization-beam-combiner device described above. The remainder of thesystem then operates exactly as the previously described embodiment.

FIG. 11 shows an all single-mode (SM) fiber (i.e. not PM fiber) spinnermodule. By adjusting the polarization controller (LeFevre Loops 60)until no fringes are observed on the nulling detector 62 as the laser isswept, orthogonality of the polarization states in both arms of the“spinner” is guaranteed. The polarization state in one arm is, however,completely arbitrary.

Calibration of a single Spinner Optical Vector Analyzer

In order to describe the calibration procedure, it will be necessary toreference specific points of the optical network within one embodimentof the optical vector analyzer. A schematic diagram of the relevantportion of the network appears in FIG. 18 where the couplers are 50/50 3dB fused-tapered, wavelength flattened couplers. In order to calibrateout the nonideal characterizations of the system, it is necessary totemporarily break one optical path in the spinner embodiment shown inFIG. 18. An optical switch 66 is therefore placed in the c-d path sothat this break can be made and the connection reestablished for normaloperation. Additionally, although the polarization controller is shownin the fiber f-i, it could also be located at other positions such asthe k-l fiber.

Before performing any measurements, and after aligning the optics, twomeasurement scans are conducted with no DUT attached. The first scan isdone with the spinner switch open, and the DC signals on the detectorsat points w and x are recorded. These DC signals are equal to theoptical power incident on each detector multiplied by the gains of thedetectors and their supporting electronics, and are frequency-dependent.We will denote them asS _(w) ^(open)(ω)=g _(w)(ω)P _(w) ^(open)(ω)  Eqn. 40andS _(x) ^(open)(ω)=g _(x)(ω)P _(x) ^(open)(ω)  Eqn. 41where P, g, and S refer to optical power, gain, and measured signal,respectively, and the subscripts refer to the two detectors. Thesuperscript is a reminder that this information was acquired with thespinner switch open. In order for polarization-dependent loss to beproperly calibrated, g_(W)(ω) and g_(X)(ω) must be equal. When thespinner switch is closed and a measurement is made, the optical signalat each detector will contain an AC term and a DC term:S _(w) ^(closed)(ω)[P _(w) ^(closed, dc)(ω)+P _(w) ^(closed, ac)(ω)e^(iωτ)]  Eqn. 42S _(x) ^(closed)(ω)=g _(x)(ω)[P _(x) ^(closed, dc)(ω)+P _(x)^(closed, ac)(ω)e ^(iωτ)]  Eqn. 43

In the above expressions ω is the optical frequency and τ is thedifference between the times for an optical signal to propagate frompoint b to point e and from point c to point d. By taking the Fouriertransform of these signals, the AC and DC terms can be separated, andthen inverse transforms will bring the information back into thefrequency domain. We obtain the following information from this scan:S _(w) ^(closed, dc)(ω)=g _(w)(ω)P _(w) ^(closed, dc)(ω)  Eqn. 44S _(x) ^(closed, dc)(ω)=g _(x)(ω)P _(x) ^(closed, dc)(ω)  Eqn. 45S _(w) ^(closed, ac)(ω)=g _(w)(ω)P _(w) ^(closed, ac)(ω)  Eqn. 46S _(x) ^(closed, ac)(ω)=g _(x)(ω)P _(x) ^(closed, ac)(ω)  Eqn. 47where the superscripts now indicate both (a) which peak of the Fouriertransform was selected, and (b) that the spinner switch was closedduring data acquisition. We now define the following calibrationquantities derived from these two scans:C ₁(ω)=√{square root over (S _(w) ^(open))}e ^(i(∠S) ^(w) ^(closed, ac)^(−∠S) ^(x) ^(closed, ac) ⁾  Eqn. 48C ₂(ω)=√{square root over (S_(x) ^(open))}  Eqn. 49C ₃(ω)=√{square root over (S_(w) ^(closed, dc) −S _(w) ^(open))}  Eqn.50C ₄(ω)=√{square root over (S_(x) ^(closed, dc) −S _(x) ^(open))}  Eqn.51

Once the above information has been obtained, it will be used to divideall subsequent measurements in the following way. If the raw OpticalVector Analyzer Jones matrix measurement yields the matrix$\begin{matrix}\left\lceil \quad\begin{matrix}{a(\omega)} & {b(\omega)} \\{c(\omega)} & {d(\omega)}\end{matrix}\quad \right\rceil & \text{Eqn.~~52}\end{matrix}$then the matrix that will be used for subsequent calculations will be$\begin{matrix}\left\lbrack \quad\begin{matrix}{a/C_{1}} & {b/C_{3}} \\{c/C_{2}} & {d/C_{4}}\end{matrix}\quad \right\rbrack & \text{Eqn.~~53}\end{matrix}$

During a measurement scan, the detector 62 at point h acquires data atthe same time as the detectors 58 and 56 at points w and x,respectively. This data has the same form as Eqs. 42 and 43, and the ACcomponent can be extracted in the same way. We will call this resultS_(h) ^(ac)(ω), and multiply the Jones matrix by the phase of S_(h)^(ac)(ω) as follows: $\begin{matrix}\left\lbrack \quad\begin{matrix}{\frac{a}{C_{1}}e^{- {i\angle S}_{h}^{ac}}} & {\frac{b}{C_{3}}e^{- {i\angle S}_{h}^{ac}}} \\{\frac{c}{C_{2}}e^{- {i\angle S}_{h}^{ac}}} & {\frac{d}{C_{4}}e^{- {i\angle S}_{h}^{ac}}}\end{matrix}\quad \right\rbrack & \text{Eqn.~~54}\end{matrix}$

The next step in calibration is to perform a measurement using a fiberpatchcord as the DUT. The resulting matrix, upon being divided by thecalibration quantities as in Eqns. 48-51, is stored in memory and iscalled the reference matrix. It will be denoted as $\begin{matrix}{{\overset{\_}{M}}_{R} = \begin{bmatrix}{\frac{a^{\prime}}{C_{1}}\quad{\mathbb{e}}^{{- {\mathbb{i}}}\quad\angle\quad S_{h}^{{a\quad c},}}} & {\frac{b^{\prime}}{C_{3}}\quad{\mathbb{e}}^{{\mathbb{i}}\quad\angle\quad S_{h}^{{a\quad c},}}} \\{\frac{c^{\prime}}{C_{2}}\quad{\mathbb{e}}^{{- {\mathbb{i}}}\quad\angle\quad S_{h}^{{a\quad c},}}} & {\frac{d^{\prime}}{C_{4}}\quad{\mathbb{e}}^{{\mathbb{i}}\quad\angle\quad S_{h}^{{a\quad c},}}}\end{bmatrix}} & {{Eqn}.\quad 55}\end{matrix}$

Once the reference matrix has been acquired, the instrument is nowconsidered to be calibrated. All subsequent measured matrices (in theform of Eqn. 54) are multiplied on the right by the inverse of M_(R) toyield the final measured Jones matrix J for the DUT, where:$\begin{matrix}{\overset{\_}{J} = {\quad\quad{{\frac{1}{{a^{\prime}\quad d^{\prime}} - {b^{\prime}\quad c^{\prime}}}\left\lbrack \quad\begin{matrix}{\frac{a}{C_{1}}\quad{\mathbb{e}}^{{- {\mathbb{i}}}\quad\angle\quad S_{h}^{{a\quad c},}}} & {\frac{b}{C_{3}}\quad{\mathbb{e}}^{{\mathbb{i}}\quad\angle\quad S_{h}^{{a\quad c},}}} \\{\frac{c}{C_{2}}\quad{\mathbb{e}}^{{- {\mathbb{i}}}\quad\angle\quad S_{h}^{{a\quad c},}}} & {\frac{d}{C_{4}}\quad{\mathbb{e}}^{{\mathbb{i}}\quad\angle\quad S_{h}^{{a\quad c},}}}\end{matrix} \right\rbrack}\quad{\quad\left\lbrack \quad\begin{matrix}{\frac{d^{\prime}}{C_{4}}\quad{\mathbb{e}}^{{- {\mathbb{i}}}\quad\angle\quad S_{h}^{{a\quad c},}}} & {{- \frac{b^{\prime}}{C_{3}}}\quad{\mathbb{e}}^{{\mathbb{i}}\quad\angle\quad S_{h}^{{a\quad c},}}} \\{{- \frac{c^{\prime}}{C_{2}}}\quad{\mathbb{e}}^{{- {\mathbb{i}}}\quad\angle\quad S_{h}^{{a\quad c},}}} & {\frac{a^{\prime}}{C_{1}}\quad{\mathbb{e}}^{{\mathbb{i}}\quad\angle\quad S_{h}^{{a\quad c},}}}\end{matrix}\quad \right\rbrack}}}} & {{Eqn}.\quad 56}\end{matrix}$

All Coupler/Polarization Controller Embodiment

The polarization beam-splitter 54 remaining in the design in thedescription above not only adds cost, but places very tight restrictionson the coupler tolerances in the spinner interferometer. A problem withthe above embodiment is that a polarization controller 52 and polarizingbeam-splitter 54 would be required for each additional receiving channelif multiple detection channels were required.

These difficulties can be resolved using a double spinner embodimentwithout polarization control as shown in FIGS. 12 & 13. The light source14 supplies either a varying frequency light (for example, from atunable laser source sweeping through the frequency of interest) or abroadband light (including the frequency range of interest) to twospinners 16 a and 16 b. It is understood that the reference path in theform of the dotted line 13 (shown in FIG. 1) would be needed in thevariable frequency light source embodiment, it has been eliminated fromFIG. 12 to illustrate a broadband light embodiment with an opticalspectrum analyzer (OSA), in this instance a grating spectrometer 68.Other OSA's include a Fourier-Transform spectrometer and a scanningFabry-Perot spectrometer.

In the FIGS. 12 & 13 embodiments, the output of each spinner provideslight whose polarization varies linearly with frequency, the differencebetween the two spinners is that the rate of change of polarization withrespect to a change in frequency is different. This difference in therate of change can be defined by a path length difference, or othercharacteristics of the spinner.

The outputs of spinners 16 a and 16 b are applied to the DUT 10, and thereference path 18, respectively. The two outputs are connected to thecoupler 22 with the output detected and applied to the microprocessor 26as before. However, because of the difference in polarization rate ofchange, there is no need to utilize a polarizer in the processing of theoutputs. As with the embodiment of FIG. 1, if the narrow linewidthsource, such as a tunable laser, is used, a light sample is supplied tothe spectral acquisition block 28.

One specific embodiment of the double spinner optical vector analyzer isshown in FIG. 13. One Mach-Zender interferometer is used for eachspinner. One arm serves as the reference, and the other arm includes thedevice under test. Each interaction between the four polarizations canbe made to have a unique apparent location in the transform of theinterferometer fringes. In the FIG. 13 embodiment of the presentinvention, there is shown a coupler/polarization-controller network forfull Jones matrix measurements measured by single device detector 64.Although adjustment of the fringes is not absolutely necessary, in apreferred embodiment, the interference terms occurring at L1, L1+L2,L1−L3 and L1−L3+L2 on detector 62 are adjusted to be non-zero usingpolarization controller 52.

Two of the polarization interactions are between different arms of thesame spinner interferometer. These interactions are nulled using thepolarization controllers in the interferometers (shown as LeFevre Loops60 to distinguish from the nulling polarization controller 52 althoughthey may all be LeFevre Loops). There are then four interactionsremaining, and the four interactions are measurements of the four Jonesmatrix elements. Each matrix element is scaled by constant. Thesescaling values can be measured relatively easily, a and, since they aredetermined by coupler splitting-ratios and splice losses, they should bestable over very long periods of time. The ability to calibrate eachpath loss out of the measurement should make it possible to obtain PDLmeasurements accurate to better than 0.05 dB.

FIG. 14 is an illustration of the amplitude versus frequency of theFourier transform of the two peaks resulting from interference in thesmaller interferometers in FIG. 13. By making the differential delay ineach interferometer different, due to the increased path length of L1,the interference terms for each is readily separable.

A further advantage of this measurement method is the ability to use asingle detector 64 for the measurement. As a result, gain matchingbetween multiple detectors is not an issue, and relatively low precision(adjustable gain) components can be used. The use of a single devicedetector 64 also reduces the channel count required for a functioningsystem from four to three, meaning that a standard 4-channel board willnow support a transmission and return-loss measurement.

FIG. 15 shows the amplitude versus frequency of the Fourier transform ofthe interference fringes at the device detector 64. Note that thedifferential delays for each of the small interferometers must beunequal to prevent the overlap of matrix terms, and that the optimaldifference is that one delay should be twice the other. The spectralmatrix entries are obtained by applying an inverse Fourier transform toeach of the time domain responses.

Including all four elements in a single channel measurement does havethe disadvantage of requiring more temporal range, and greaterseparation between the device, and any possible reflections (primarilyconnector reflections). In general, if a five nanosecond (5 ns) responseis allowed (equivalent to 200 Mz sample spacing), then the fiber leadsmust be a minimum of 2 meters long. 3 meter leads would permit a 7 nsresponse time.

Scalability-Multiple Test Station Architecture

Because the double-Mach-Zender configuration of FIG. 13 does not haveany defined polarization states, and thus no polarization controllerassociated with the measurement detector, it is easily scalable. Perhapsthe first way in which this scaling can be applied would be to measuremultiple outputs of a single device such as a Dense Wavelength DivisionMultiplexer (DWDM), a de-multiplexer, or an optical switch. FIG. 16 is aschematic of a single source, multiple detector, Jones matrixmeasurement system. Note that each additional detection channels requireonly a coupler and a detector 64, and no polarizing or polarizationcontrol elements.

A second application of the scalability of the double-Mach-Zenderconfiguration would be to distribute the source light and themeasurement light to multiple measurement stations for a plurality ofdevices under test (DUT 10) in a single facility. In this way the costof the laser could be spread over multiple measurement stations,resulting in an extremely cost effective solution. FIG. 17 is aschematic of a multiple device/single source Jones Matrix measurementsystem. Note that each additional detection channel requires only acoupler and a detector, and no polarizing or polarization controlelements.

In the view of the various embodiments and discussion of the presentinvention noted above, many variation and subsititutions of elements forthose disclosed will be obvious to one or ordinary skill in the art.Accordingly, the invention is limited only by the claims appendedhereto.

1. An optical vector analyzer for analyzing the characteristics of afiber-optic device under test (DUT) over a frequency range of interest,comprising: a source of light having an optical frequency content oversaid frequency range of interest, for feeding a spinner, said spinnerconfigured to provide a spinner light output having a polarization statewhich varies linearly with said frequency range, said spinner lightoutput coupled as an input to both said DUT and a reference path; a beamcombiner for adding combining a light output from said reference pathand a light output from said DUT for a plurality of frequencies in saidfrequency range of interest and providing an output indicative ofoptical power, in two orthogonal polarization states, of said combinedlight; and microprocessor responsive to said power outputs andprogrammed to: digitize said power outputs over a plurality offrequencies in said frequency range of interest, derive respectivecurves from said digitized power outputs, calculate the Fouriertransform of said respective curves, and derive from said Fouriertransforms, one or more arrays of constants for a Jones matrix, therebycharacterizing said device under test.
 2. An optical vector analyzeraccording to claim 1, wherein said source of light is comprised of anarrow linewidth tunable source of light.
 3. An optical vector analyzeraccording to claim 2, wherein said tunable source of light is a tunablelaser.
 4. An optical vector analyzer according to claim 3, wherein saidmicroprocessor is also, responsive to said source of light.
 5. Anoptical vector analyzer according to claim 1, wherein said source oflight is a broadband optical source.
 6. An optical vector analyzeraccording to claim 1, wherein said beam combiner of includes: a coupleradding the reference path output and the DUT output; and a polarizersplitting the added outputs into said two orthogonal polarized outputs.7. An optical vector analyzer according to claim 6, wherein said coupleris a bulk-optic beam splitter.
 8. An optical vector analyzer accordingto claim 6, wherein said coupler is a fused tapered coupler.
 9. Anoptical vector analyzer according to claim 1, wherein saidmicroprocessor includes a spectral acquisition device for measuring theoptical power of the light in the two orthogonal polarization states.10. An optical vector analyzer according to claim 1, wherein saidmicroprocessor includes an optical spectrum analyzer for measuring theoptical power output in the frequency range of interest.
 11. An opticalvector analyzer according to claim 9; wherein said source of light is atunable laser-, and a sample of said laser light is provided to saidspectral acquisition device, said spectral acquisition device including:a Michelson interferometer supplied with said laser light sample forgenerating a trigger light signal; a trigger detector, responsive tosaid trigger light signal, providing a power acquisition trigger signal;and two power detectors, each power detector measuring the optical powerin one of said tow orthogonal polarization states.
 12. An optical vectoranalyzer according to claim 11, wherein said interferometer includes: atwo way coupler for splitting said laser light sample into two opticalsignals; two optical paths, each path having two ends, one of said twoends receiving one of said two optical signals from said coupler, one ofsaid optic paths is longer than the other of said optical paths; and twoFaraday rotator mirrors, one of said mirrors connected to the other endof each of said two optical paths, wherein said laser light sample isphase delayed in said longer path relative to the shorter path andreflected by said mirrors back to said coupler, wherein said reflectedsignals are combined and are coupled to said trigger detector.
 13. Anoptical vector analyzer according to claim 12, wherein said spectralacquisition device further includes: a coupler to provide a portion ofsaid laser light sample; and a frequency monitor, responsive to saidportion of said laser light sample, for providing an output indicativeof the wavelength of said laser light sample.
 14. An optical vectoranalyzer according to claim 1, wherein said combiner includes: apolarization controller for adjusting the polarization of the recombinedportions of light; a polarizing beam splitter, responsive to saidpolarization controller, for splitting said recombined light into x- andy- polarization components; and s- and p- detectors, responsive to saidx- and y- polarization components, respectively, for providing anelectrical signal indicative of the amplitude of the x- and y-polarization components.
 15. An optical vector analyzer according toclaim 14, wherein said polarization controller is adjustable to providea nulled alignment in which the relative phase of the two states ofpolarization at the coupler does not affect a power splitting ratio atsaid polarization beam splitter.
 16. An optical vector analyzeraccording to claim 14, wherein said polarization controller isadjustable to provide a maximum contrast alignment in which the relativephase of the two states of polarization at the coupler provides amaximum amount of power at one of the detectors and, at the same time,provides a minimum amount of power at the other of the detectors.
 17. Aspinner for modifying light from a source into light having apolarization which varies linearly with respect to variations in opticalfrequency of the source light over a frequency range of interest, saidspinner comprising: a splitter for splitting said light from said sourceinto two portions of light; two separate light paths, each path suppliedwith a portion of said light, each light path having a Jones matrixwhich is independent of wavelength of said light, each path having aJones matrix different from the Jones matrix of the other path suchthat, at the end of each path, light transmitted along the two paths ismutually orthogonal, and a spinner combiner for combining light fromsaid two paths, where a combined light output has a polarization statewhich varies linearly with frequency variation of said light from saidsource.
 18. A spinner according to claim 17, wherein said splittercomprises a polarization maintaining coupler for splitting said lightfrom said source.
 19. A spinner according to claim 17, wherein saidsplitter comprises a single mode coupler for splitting said light fromsaid source.
 20. A spinner according to claim 17, wherein said spinnerincludes at least one polarizer controller, located in at least one ofsaid two paths, for controlling polarization in at least one of said twopaths to provide mutually orthogonal light at the spinner combiner. 21.A spinner according to claim 20, wherein a portion of the combineroutput is provided to a nulling detector for providing an electricaloutput indicative of the phase relationship of light in said two paths.22. An optical vector analyzer for analyzing the characteristics of afiber-optic device under test (DUT) over a frequency range of interest,comprising: (a) a narrow linewidth tunable source of light for providinga varying optical frequency light over said frequency range of interest,said light having an initial polarization, (b) a spinner, supplied withsaid light, including: (1) a splitter for splitting said light from saidsource into two portions of light; (2) two separate light paths, onepath comprising a long path and the other path comprising a short pathrelative to said long path, each path supplied with one portion of saidlight, each light path having a Jones matrix which is independent ofwavelength of said light, each path having a Jones matrix different fromthe Jones matrix of the other path such that, at the end of each path,light transmitted along the two paths is mutually orthogonal, (3) aspinner combiner for combining light from said two paths, where, as aresult of the path length difference, a combined light output from thecombiner has a polarization state which varies linearly with frequencyvariation of said light from said source, said light provided as aninput to both said DUT and a reference path; (c) a beam combiner foradding light from said reference path and from said DUT for a pluralityof frequencies in said frequency range of interest and for providing anoutput indicative of optical power, in two orthogonal polarizationstates, of said combined light; (d) a spectral acquisition unit formeasuring said optical power with respect to wavelength for saidplurality of frequencies; and (e) a microprocessor, responsive to saidmeasured power and programmed to: (1) digitize said measured power forsaid frequencies, (2) derive respective curves from said digitized powermeasurements, and (3) calculate the Fourier transform of said respectivecurves, and (4) derive from said Fourier transforms, one or more arraysof constants for said Jones matrix, thereby characterizing said deviceunder test.
 23. An optical vector analyzer according to claim 22,wherein said tunable source of light is includes a laser.
 24. An opticalvector analyzer according to claim 22, wherein said splitter comprises apolarization maintaining coupler for splitting said light from saidsource.
 25. An optical vector analyzer according to claim 22, whereinsaid splitter comprises a single mode coupler for splitting said lightfrom said source.
 26. An optical vector analyzer according to claim 22,wherein said spinner includes at least one polarizer controller, locatedin at least one of said two paths, for controlling polarization in atleast one of said two paths to provide mutually orthogonal light at thespinner combiner.
 27. An optical vector analyzer according to claim 22,wherein a portion of the combiner output is provided to a nullingdetector for providing an electrical output indicative of the phaserelationship of light in said two paths.
 28. An optical vector analyzeraccording to claim 22, wherein said beam combiner includes: a couplerfor adding the reference path output and the DUT output; and a polarizerfor splitting the added outputs into said two orthogonal polarizedoutputs.
 29. An optical vector analyzer according to claim 22, whereinsaid combiner includes: a polarization controller for adjusting thepolarization of the recombined portions of light; a polarizing beamsplitter, responsive to said polarization controller, for splitting saidrecombined light into x- and y- polarization components; and s- and p-detectors, responsive to said x- and y- polarization components,respectively, for providing an electrical signal indicative of theamplitude of the x- and y- polarization components.
 30. An opticalvector analyzer according to claim 29, wherein said polarizationcontroller is adjustable to provide a maximum contrast alignment inwhich the relative phase of the two states of polarization at thecoupler provides a maximum amount of power at one of the detectors and,at the same time, provides a minimum amount of power at the other of thedetectors.
 31. An optical vector analyzer according to claim 22, whereinsaid coupler is a fused tapered coupler.
 32. An optical vector analyzeraccording to claim 22, wherein said microprocessor includes a spectralacquisition device for measuring the optical power of the light in thetwo orthogonal polarization states.
 33. An optical vector analyzeraccording to claim 32, wherein said source of light is a tunable laser-,and a sample of said laser light is provided to said spectralacquisition device, said spectral acquisition device includes: aMichelson interferometer supplied with said laser light sample forgenerating a trigger light signal; a trigger detector, responsive tosaid trigger light signal, providing a power acquisition trigger signal;and two power detectors, each power detector measuring the optical powerin one of said tow orthogonal polarization states.
 34. An optical vectoranalyzer according to claim 33, wherein said interferometer includes: atwo way coupler for splitting said laser light sample into two opticalsignals; two optical paths, each path having two ends, one of said twoends receiving one of said two optical signals from said coupler, one ofsaid optic paths is longer than the other of said optical paths; and twoFaraday rotator mirrors, one of said mirrors connected to the other endof each of said two optical paths, wherein said laser light sample isphase delayed in said longer path relative to the shorter path andreflected by said mirrors back to said coupler, wherein said reflectedsignals are combined and are coupled to said trigger detector.
 35. Anoptical vector analyzer according to claim 34, wherein said spectralacquisition device further includes: a coupler to provide a portion ofsaid laser light sample; and a frequency monitor, responsive to saidportion of said laser light sample, for providing an output indicativeof the wavelength of said laser light sample.
 36. An optical vectoranalyzer for analyzing the characteristics of a fiber-optic device undertest (DUT) over a frequency range of interest, comprising: (a) a sourceof broadband light having a frequency band over said frequency range ofinterest, said light having an initial polarization, (b) a spinner,supplied with said light, including: (1) a splitter for splitting saidlight from said source into two portions of light; (2) two separatelight paths, one path comprising a long path and the other pathcomprising a short path relative to said long path, each path suppliedwith one portion of said light, (3) a spinner combiner for orthogonallycombining light from said two paths, where, as a result of the pathlength difference, a combined light output from the combiner has apolarization state which varies linearly with frequency of said lightfrom said source, said light provided as an input to both said DUT and areference path; (c) a beam combiner for adding light from said referencepath and from said DUT for a plurality of frequencies in said frequencyrange of interest and providing a beam combiner output; (d) an opticalspectrum analyzer, responsive to said beam combiner output, forachieving a minimum resolution bandwidth of no more than one fourth thebandwidth of said frequency range of interest and providing an output;and (e) a microprocessor, responsive to said spectrum analyzer outputand programmed to: (1) derive respective curves from said analyzeroutput; (2) calculate the Fourier transform of said respective curves,and (3) derive from said Fourier transforms, one or more arrays ofconstants for a Jones matrix, thereby characterizing said device underquestion test.
 37. An optical vector analyzer according to claim 36,wherein said splitter comprises a polarization maintaining coupler forsplitting said light from said source.
 38. An optical vector analyzeraccording to claim 36, wherein said splitter comprises a single modecoupler for splitting said light from said source.
 39. An optical vectoranalyzer according to claim 36, wherein said spinner includes at leastone polarizer controller, located in at least one of said two paths, forcontrolling polarization in at least one of said two paths to providemutually orthogonal light at the spinner combiner.
 40. An optical vectoranalyzer according to claim 39, wherein a portion of the combiner outputis provided to a nulling detector for providing an electrical outputindicative of the phase relationship of light in said two paths.
 41. Anoptical vector analyzer according to claim 36, wherein said beamcombiner includes: a coupler for adding the reference path output andthe DUT output; and a polarizer for splitting the added outputs intosaid two orthogonal polarized outputs.
 42. An optical vector analyzeraccording to claim 36, wherein said combiner includes: a polarizationcontroller for adjusting the polarization of the recombined portions oflight; a polarizing beam splitter, responsive to said polarizationcontroller, for splitting said recombined light into x- and y-polarization components; and s- and p- detectors, responsive to said x-and y- polarization components, respectively, for providing anelectrical signal indicative of the amplitude of the x- and y-polarization components.
 43. An optical vector analyzer according toclaim 36, wherein said optical spectrum analyzer includes a gratingspectrometer.
 44. An optical vector analyzer according to claim 36,wherein said microprocessor includes a spectral acquisition device formeasuring the optical power of the light in the two orthogonalpolarization states.
 45. An optical vector analyzer for analyzing thecharacteristics of a fiber-optic device under test (DUT) over afrequency range of interest, comprising: (a) a source of light having anoptical frequency content over said frequency range of interest, saidsource of light providing two mutually coherent light beams, each ofsaid light beams feeding a spinner for providing a spinner light outputhaving a polarization state which varies linearly with said frequency,and said spinner light outputs having different rates of change ofpolarization with respect to change of frequency of the light beam, oneof said spinner light outputs comprises an input to said DUT and theother of said spinner light outputs comprises an input to a referencepath; (b) a beam combiner for combining light output from said referencepath and light output from said DUT over said frequency range ofinterest and providing a detected output; and (c) a microprocessor,responsive to said detected output and programmed to (1) digitize saiddetected output over a plurality of frequencies at said frequency rangeof interest, (2) derive respective curves from said digitized outputs,(3) calculate the Fourier transform of said respective curves, and (4)derive from said Fourier transforms, one or more arrays of constants fora Jones matrix, thereby characterizing said device under test.
 46. Anoptical vector analyzer according to claim 45, wherein a portion of thecombiner output is provided to a nulling detector for providing anelectrical output indicative of the phase relationship of light in saidtwo paths.